1. Technical Field
Embodiments of the subject matter disclosed herein generally relate to methods and systems and, more particularly, to mechanisms and techniques for smoothing a velocity model that has velocity discontinuities.
2. Discussion of the Background
Seismic data acquisition and processing generate a profile (image) of geophysical structures under the seafloor or subsoil. While this profile does not provide an accurate location for oil and gas reservoirs, it suggests, to those trained in the field, the presence or absence of them. Thus, providing a high-resolution image of the structures under the seafloor/subsoil is an ongoing process.
To construct images of the subsoil (or subsurface), geologists or geophysicists conventionally use wave emitters (sources) placed on the surface, for example. For the case of marine seismic surveys, the wave emitters are towed by a vessel at or under the surface of the water. Such emitters emit waves (e.g., acoustic waves) which propagate through the subsoil (and water for the marine seismic) and which are reflected on the surfaces of the various layers thereof (reflectors). Waves reflected to the surface are recorded as a function of time by receivers (which are towed by the same vessel or another vessel for the marine seismic or lay on the ocean bottom). The signals received and recorded by the receivers are known as seismic traces.
Based on the seismic traces, an image of the surveyed subsurface is generated. One ingredient for processing the seismic traces is the depth velocity model. Most ray-based migration and tomography methods require a certain degree of smoothness in the depth velocity models. A drawback of the conventional smoothing is the introduction of errors in the travel-times at the discontinuities of the velocity models. A travel-time is considered to be the time necessary for an emitted wave to travel from the source to a reflector and back to a receiver. These errors are offset-dependent and they cause errors in both depth location of the imaged reflectors and the residual move-out (RMO).
In velocity model-building for pre-stack depth migration (PSDM), the velocity models are commonly built by layer-stripping with discontinuous velocities across the horizons. An example of such a model is shown in FIG. 1, in which various interfaces 10, 12, 14, 16, and 18 are distributed at various depths (on the z axis). A region between two consecutive interfaces, e.g., 12 and 14, has a given velocity v2. The velocity changes rather abruptly from one depth D1 to another depth D2, as illustrated in FIG. 2. These velocity models are usually inserted into the migration algorithms as regularly sampled 3D grids. Existing algorithms, such as ray-tracing (see, e.g., Oerveny V. “Seismic Ray Theory,” Cambridge Univ. Press, Cambridge, 2001) used in Kirchhoff migration, or beam migration, have difficulties dealing with the abrupt velocity variations. Thus, a technique for smoothing the velocity models is used. Current practice is to achieve the smoothing by applying a Gaussian or similar bell-shaped filter. For anisotropic models, the smoothing is applied independently on each of the five parameters describing the velocity field, 1/v, δ, ε, dip1, dip2, where v is the wave velocity along the symmetry axis, δ and ε are the Thomsen parameters, and dip1 and dip2 describe the dip of the plane perpendicular to the symmetry axis.
In conventional imaging processing, the main direction of anisotropy of the subsurface is often assumed to be equal to the structural dip that follows the geology of the subsurface. When referring to transverse isotropy, this case is often referred to as Structural Transverse Isotropy (STI). In this regard, FIG. 3 shows a portion of a subsurface 20 having various layers 22, 24, 26. The tilt axis 28 for a portion 30 of layer 22 is perpendicular (for most cases) to the surface of the portion 30. The tilt axis is picked from a seismic migrated cube usually obtained by depth migration in an isotropic or Vertical Transverse Isotropy (VTI) or STI or Tilted Transverse Isotropy (TTI) model. The picked tilt axis is usually inserted into the velocity model to describe its main symmetry axis. This will affect wave propagation in this velocity model.
One of the disadvantages of the conventional way of smoothing the velocity model is that migrated events are shifted in comparison to the un-smoothed model at the velocity discontinuities. This shift is dependent on the size of the velocity variation, the size of the smoothing operator, and the offset. Thus, the conventional processing algorithms have a smoothing-induced RMO which may create artefacts in the velocity analysis.
Several solutions to this problem have been proposed in the art. One approach proposes adding explicit horizons in the ray-tracing process and using Snell's law in the transmission of rays (see, for example, Vinje et al., “Estimation of multivalued arrivals in 3D models using wavefront construction,” Part I, Geophysical Prospecting, 1996, 44, 819-842, or Hobro et al., “Direct Representation of Complex, High-contrast Velocity Features in Kirchhoff PreSDM Velocity Models,” 70th EAGE Conference & Exhibition, Extended Abstracts, 2008).
Another approach was proposed by Baina et al., “How to cope with smoothing effect in ray based PSDM?” 68th EAGE Conference and Exhibition, Extended Abstracts, 2006. This approach combines two models, a smoothed one and a non-smoothed one. The authors used a criterion from a Hamiltonian ray formulation leading to preservation of depths and RMO.
To summarize, most ray-based migration and tomography methods require a certain degree of smoothness of the depth velocity model. Because smoothing changes the velocity model, it is generally difficult to preserve the travel-time between all pairs of points in the model. Using conventional smoothing, the travel-time errors are particularly large at the discontinuities of the velocity model. These errors are offset-dependent and they cause errors in both depth and RMO of depth migrated images. Thus, it would be desirable to provide systems and methods that avoid the afore-described problems and drawbacks.